A Self‐Supervised Learning Framework for Seismic Low‐Frequency Extrapolation

Abstract Full waveform inversion (FWI) is capable of generating high‐resolution subsurface parameter models, but it is susceptible to cycle‐skipping when the data lack low‐frequency components. Unfortunately, such components (<5.0 Hz) are often tainted by noise in real seismic exploration, which hinders the application of FWI. To address this issue, we develop a novel self‐supervised low‐frequency extrapolation method that does not require labeled data, enabling neural networks to be trained directly on real data. In the proposed approach, the neural network training is divided into two stages: warm‐up and iterative data refinement (IDR). In the IDR stage, the pseudo‐labels for the current epoch are derived from the predictions made by the network trained in the previous epoch on the original observed data. The IDR stage gradually narrows the gap between the predicted pseudo‐label and the ideal ground truth, thereby enhancing the network's low‐frequency extrapolation performance. This paradigm effectively addresses the significant generalization gap often encountered using supervised learning techniques, which are typically trained on synthetic data. We validate the effectiveness of our method on both synthetic and field data. The results demonstrate that our method effectively extrapolates low‐frequency components, aiding in circumventing the challenges of cycle‐skipping in FWI. Meanwhile, by integrating a self‐supervised denoiser, our method effectively and simultaneously performs denoising and low‐frequency extrapolation on noisy data. Furthermore, we showcase the potential application of our method in extending the ultralow frequency components of the large‐scale collected earthquake seismogram.